Whether spiritual means something beyond the physical, or just societal and personal subconscious, there exists elements of life beyond our personal sight. We observe nature and humanity and find patterns. Principles may be truer or higher patterns beyond those one's wisdom has gleaned from neural nets of experience. Maybe a person's greatness or power is a reflection of their ability to surf these truth waves.
I think of Mahatma Gandhi who without formal position or excessive ability choose a path altering national and world events. Now was his spirituality-- natural, social or physical law, or was it something less tangible? Does it matter? The fact is we can observe the life and his influence, regardless of theories.